1. Field of the Invention
The present invention relates to a method and a program for calculating the maximum depth of cut without any self-excited vibration, and more particularly, to a method for preliminarily anticipating a stable machining condition when three-dimension-contour machining is performed while a cutting tool is rotatably moved by a machine tool so as to prevent a self-excited vibration that causes tool breakage or deterioration in machining accuracy.
2. Description of the Related Art
In the case of milling by means of a rotating tool, the low rigidity of the tool or a workpiece may cause a relative vibration between the tool and the workpiece. The relative vibration between a tool and a workpiece is caused by a forced vibration or a self-excited vibration.
In the case of the relative vibration due to a forced vibration, the cutting edge of the rotating tool passes through the workpiece, thereby causing milling force acting between the tool and the workpiece; the milling force produces a relative displacement. In this situation, the tool or the workpiece vibrates at a milling frequency determined by the product of the multiplication of the tool rotation speed by the number of the cutting edges; when the vibration is large, noise or the vibration of the machine tool is caused.
In contrast, in the case of the relative vibration due to a self-excited vibration, a vibration is caused at a frequency close to the natural frequency of a mechanical system consisting of a tool, a machine tool, a workpiece, and the like. The relative vibration due to a self-excited vibration has a characteristic that a vibration does not start immediately after the commencement of milling, but with the progress of the milling, the vibration gradually becomes large. In many cases of the relative vibration due to a self-excited vibration, the natural frequency of a mechanical-system is generally several hundreds Hz to several kHz, and the tone of the noise due to the vibration is relatively high.
The self-excited vibration has been modeled through the regeneration theory proposed by Tlusty et al., and a method therefor was established in which numerical-analysis anticipation is performed. The regeneration effect denotes the phenomenon that a tool vibration, produced due to the fluctuation in milling thickness in the case where milling is performed by a cutting edge that passes through a wavefront that has been formed through one-period-previous vibrating milling by the cutting edge, increases with the progress of the milling.
The stability limit of the milling self-excited vibration is determined by the radial depth of cut, axial depth of cut, and the like, among machining conditions. In general, the axial depth of cut that, with the radial depth of cut fixed to a given value, corresponds to the stability limit of a self-excited vibration is referred to as stability-limit depth of cut. By preliminarily anticipating the stability-limit depth of cut so as to create an NC program, modification of the NC program due to the occurrence of a vibration becomes unnecessary, whereby the number of man-hours can significantly be reduced.